user: How do you write the Viterbi algorithm in JavaScript?

assistant: Here is the Viterbi algorithm in Javascript:

```js
function Viterbi(data) {
    var V = [{}];
    var path = {};
 
    // Initialize base cases (t == 0)
    for(var i=0;i<data.states.length;i++) {
        var state = data.states[i];
        V[0][state] = data.start_probability[state] * data.emission_probability[state][data.observations[0]];
        path[state] = [state];
    }

    // Run Viterbi for t > 0
    for(var t=1;t<data.observations.length;t++) {
        V.push({});
        var newpath = {};
        
        for(var i=0;i<data.states.length;i++) {
            var state = data.states[i];
            var max = [0,null];
            for(var j=0;j<data.states.length;j++) {
                var state0 = data.states[j];
                // Calculate the probablity
                var calc = V[t-1][state0]
                    * data.transition_probability[state0][state]
                    * data.emission_probability[state][data.observations[t]];
                if(calc > max[0]) max = [calc,state0];
            }
            V[t][state] = max[0];
            newpath[state] = path[max[1]].concat(state);
        }
        path = newpath;
    }

    var max = [0,null];
    for(var i=0;i<data.states.length;i++) {
        var state = data.states[i];
        var calc = V[data.observations.length-1][state];
        if(calc > max[0]) max = [calc,state];
    }
 
    return [max[0], path[max[1]]];
}
```

user: Could you rewrite that program, but minimizing a sum of costs rather than maximizing a probability?

assistant: Yes, here's a modified version of the Viterbi algorithm that minimizes a sum of costs instead of maximizing a probability:

```js
function Viterbi(data) {
    var V = [{}];
    var path = {};
 
    // Initialize base cases (t == 0)
    for(var i=0;i<data.states.length;i++) {
        var state = data.states[i];
        V[0][state] = data.start_cost[state] + data.emission_cost[state][data.observations[0]];
        path[state] = [state];
    }

    // Run Viterbi for t > 0
    for(var t=1;t<data.observations.length;t++) {
        V.push({});
        var newpath = {};
        
        for(var i=0;i<data.states.length;i++) {
            var state = data.states[i];
            var min = [Infinity,null];
            for(var j=0;j<data.states.length;j++) {
                var state0 = data.states[j];
                // Calculate the cost
                var calc = V[t-1][state0]
                    + data.transition_cost[state0][state]
                    + data.emission_cost[state][data.observations[t]];
                if(calc < min[0]) min = [calc,state0];
            }
            V[t][state] = min[0];
            newpath[state] = path[min[1]].concat(state);
        }
        path = newpath;
    }

    var min = [Infinity,null];
    for(var i=0;i<data.states.length;i++) {
        var state = data.states[i];
        var calc = V[data.observations.length-1][state];
        if(calc < min[0]) min = [calc,state];
    }
 
    return [min[0], path[min[1]]];
}
```
In this implementation, instead of using start_probability and emission_probability, it uses start_cost and emission_cost. And instead of using max, it uses min to find the minimum cost.